Using samples of 102 million Upsilon(1S) and 158 million Upsilon(2S) events collected with the Belle detector, we study exclusive hadronic decays of these two bottomonium resonances to (KSK+)-K-0 pi(-) and charge-conjugate (c.c.) states, pi(+) pi(-) pi(0) pi(0), and pi(+) pi(-) pi(0), and to the two-body Vector-Pseudoscalar (K*(892)0 (K) over bar (0) + c.c., K*(892)K--(+) + c.c., omega pi(0), and rho pi) final states. For the first time, signals are observed in the modes Upsilon(1S) -> K-S(0) K+ pi(-) + c.c., pi(+) pi(-) pi(0) pi(0), and Upsilon(2S) -> pi(+) pi(-) pi(0) pi(0), and evidence is found for the modes Upsilon(1S) -> pi(+) pi(-) pi(0), K-*(892)(0)(K) over bar (0) + c.c., and Upsilon(2S) -> K-S(0) K+ pi(-) + c.c. Branching fractions are measured for all the processes, while 90% confidence level upper limits on the branching fractions are also set for the modes with a statistical significance of less than 3 sigma. The ratios of the branching fractions of Upsilon(2S) and Upsilon(1S) decays into the same final state are used to test a perturbative QCD prediction for Okubo-Zweig-Iizuka- suppressed bottomonium decays.